Car won't start unless I give it gas

I own a 2001 Volvo S40. At first I had a problem getting it to stay running on the first start. Before when I started the car it would stall the first or second time. Then I would give it a little gas, let off and it would bog down under 750 rpms then jump up to 750 and run fine. The car would start great afterwards as long as I started it within a few hours. If I let it sit overnight I would run into the same problem as mentioned before. That was then and this is now. The last time the car ran I noticed the car would not fully warm up. It was like 30 degrees outside and the fans only blew cold air. The temp gauge stayed on the cold side the whole ride home (roughly 35 miles). The next day it was still about 30 degrees outside and when I went to start the car the car it stalled. I tried to start it again and gave it some gas but when I let off the gas pedal the car shut off. I tried again with the same results. The next time I keep my foot on the gas for a good minute. The car would rev up no problem but once I let off the gas the car would stall. I figured it was the cold weather. So the next it was beautiful (close to 60). I tried to start it again with the same results as the previous day. That was a few days ago. Since then, I’ve tried a few times but to no avail. Now for my moment of shame (I have no idea if this is relevant). I bought the car with 108,000 miles on it from a dealer. Since then I’ve put about 17,000 miles on it and haven’t done any maintenance to it. Absolutely none. No oil change, plugs, air filter, etc. Please don"t chastise me. I wanted to keep it to myself but am trying to be completely honest to ensure proper troubleshooting. I did check the oil level and it was ok. Also, I have about half a tank of gas in the tank. Honestly, I have no idea where to start. I believe it could be numerous issues. So if anyone could start with the most likely and or least costly, I would greatly appreciate it.

You probably have a couple of problems. The fact that your car isn’t warming up is an indication that the thermostat needs to be replaced. A coolant flush should probably be done when you replace the thermostat. The engine may need to have the air and fuel filters replaced. The engine may also need new spark plugs and wires and it is definitely overdue for an oil and oil filter change. A good mechanic can advise you on the necessity of the need for the fuel and air filters and the need for new spark plugs. The oil and filter change and thermostat are a must.

A car of this age, unknown maintenance, my guess is the air bypass valve and throttle plate need a good cleaning to help with the start-up issue.
As for the coolant not coming up to temp, Triedag is probably spot on with the thermostat being bad.